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We define and classify the analogues of the affine Kac-Moody Lie algebras forthe ring corresponding to the complex projective line minus three points. Theclassification is given in terms of Grothendieck's dessins d'enfants. We alsostudy the question of conjugacy of Cartan subalgebras for these algebras.

Three-point Lie algebras and Grothendieck's dessins d'enfants